What are the best bases and rings for this rifle?

I was considering these Leupold bases

It depends what you want to do with it.  The Rem 541S is capable of great accuracy and 1 MOA to 1.25 MOA 5 shot groups at 100 yards are the norm with a decent standard velocity or mid grade match ammo like CCI SV or Sk Standard Plus, you just need to find what it likes.

In that regard, if you want to use it to shoot plates out to 200-300 yards with a scope with finger adjustable target turrets, Burris Signature Z rings make sense, and they make them for the Leupold standard bases.   Using 5, 10 and 20 MOA inserts in the rings, those rings will allow you to put 5 MOA, 10 MOA, 15 MOA, 20 MOA, 25 MOA, 30 MOA or 40 MOA on the scope to allow you to extend the range out to 300 yards or so.

----

I have other .22 LRs I prefer for long range use, so my 541S is set up for 100-150 yards, with a similar vintage 8x Redfield target scope using standard Leupold rings.

I'm pretty sure these are medium rings:

I just use Leupold’s high gloss 1” tip off rings for the 3/8” dovetail.  They match the Leupold 2-7x rimfire scope from the same period as the rifle.  They complement the lines of the 541-S and are rock solid.

Update.  I did recently install a target scope on this same rifle.  It has a big 50mm objective lens and requires high rings.

I ended up installing the Leupold front and rear standard bases with the dovetail slot in the front base and the windage adjustment screws in the rear.  Same as depicted in DakotaFAL’s photo. Not a big fan of the style, but they are rugged and time-tested.

The setup is working well.  I understand that the front and rear base pattern on the 541-S, 541-T and Browning’s T-Bolt .22lr are the same.  Thus, any mount for the T-Bolt ought to work, too.

These are wonderfully accurate rifles, especially given their classic sporter wooden stock and barrel profile.